Sometimes people say 1/ztad ,/k 1pup rhv 6-ymgq6athat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. , 6vzauqh1y/mpktp 1/adg-r6 What is wrong with this statement?

Will the acceleration of a car be 4tkjv huw269k-vevh6 9r qo ddg2b/v,the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at thjdv6 ,9v/ o9wg262q4kk bt urve- dhhve same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does tpc sx0 rod g*,zg11yxj6 o+l6lhe car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretc6+1* cdlrzjy pl 0ogxg ,16soxh near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry*6c,dbn b cch*ap8mc8 -go-round. Which of these forces provides the centripetalbc 8 ,h8ap6c*bnc d*mc acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spilliw40x0fum -oou ph: fg:gq 9as-ng out, even at the top of the circle when th40o swhq xuo-:aff9mg0p-:gu e bucket is upside down. Explain.

How many “accelerators” do you have in your car? There 66ycda( :c .r amy4sxlg)hpo 0are at least three controls in the car which can be used to cause the car to accel x (4rch6a) lcgyo60.m :pydsaerate. What are they? What accelerations do they produce?

A child on a sled comes flyinbi40(g-w o+p, aa vu./xrldzwkjvf9 :g over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decreavl zkfx9.4wa ,r(bgovpud:+-ia0j /wse using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speed7 gv6e1wvue8iopp5 +q?

Why do airplanes bank when they turn? How ab ms.bkm*k lcg c2fpk- /e4n0.3h-xawould you compute the banking angle given its speed and radius of th2-xk .bmkhc/fnpba .c se gma*304 l-ke turn?

A girl is whirling a ball on a stringl2jxf;fcrf,;hd 9 l:i around her head in a horizontal plane. She wants to let go at preciselc i;fdhl :;l xf,92rjfy the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earts5i qzb ;y1;agpr9qu) h? If so, how large a force? gs9puzby)q ;5 q; 1raiConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass werj,xs0 (vylk3e* pvgu4e double what it is, in what ways would the Moon’s orbit bsevyv*x(k4,3 pulg0je different?

Which pulls harder gravitation p3xjh / 2i,b0jx9lafvally, the Earth on the Moon, or the Moon on the Earth? Which acceleraj,l29b iv3 xpaxj0f h/tes more?

The Sun's gravitational pull on the Earth is much larsf 9;,p gvcmqr: c+4htger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of rv+ tp;g9smch:fq,4c the Earth to the other.]

Will an object weigh more0eb:4km/yhhb t h 3(ca at the equator or at the poles? What two effects are at work? Do they oppose eb:a/tm3 hb4(c kh0eyhach other?

The gravitational forc/s b g16pb91f hutl5wr (jmt3ie on the Moon due to the Earth is only about half the force ps fb1(tlr/w69tjihug15 3m bon the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acce*bu0;jt g-iw cleration of Mars in its orbit around the Sun larger or smaller than the c;0-cuib tj*w gentripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the easa/ h.;44x kifwvbiolng.i xd8 *i:py8 xx9 1act or (b) toward the west? Consider the Ey ;:48vxn9.dx4gc*.apixx ikfihlb/a8 i 1wo arth’s rotation direction.

When will your apparent weight be tyo- o ,rt4sjc9he greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constantr jcso9ot4 y-, speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely1w,4e7s:agl nrw6og+lp:cp c affected by weightlessness. One way to simulate gravity is to shape the spaceship liken:ls7+glp:w,g 1rco a6p4c ew a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experif/zbus(u 4upma ;a+e052ei kwences “free fall” or “apparent weightlessness” between (+2sfei4zu m;p u0wka e/bu5 asteps.

The Earth moves faster in its orbit around the Sun in January than in July. Is tr-ge/pej8s- + do2 5zlewqgb; he Earthb2-5s ee g+e/j8gwlrozq ;-pd closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was di/;q:aqb7 e)mn. q cjxkscovered to have a moon. Explain ho )mjqa/;.keq7q :nxbcw this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yoa49+u r/ pqydet the M4+p a /duqyo9roon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980nak+irk i,l3- $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of amknxf9 0+0o,am4a edthe Earth in its orbit around the Sun, and dmafx 0meok ,40n aa9+the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates8bd hm.zo ;i:u uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discuzi:8m; bd uoh.s.   

  Suppose the space shuttle is in orbit 400 km from the Ec y6vb,bh t (;jt p 7pd6-8*msrihkse:arth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your -ht( b :8;vpt*k sse,cy6hb6ipd7jmr answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on t-,j:a zoum swfz1+h4dhe edge of a potter’s wheel turning at 45 rpm (revolutions per mizw,j hofumd1a:4zs+ -nute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a *:nbq/ 6nfgm7vf v4rv)tat d *string is revolved at a uniform rate in a vertical circle of r/ n76b*f 4 vtfmr:*v)tqgvdanadius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-k ef)j3 ,n +l8ck5chz+hynna1jg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this r,jaezfh+ kn183 lj ) c+nnhy5cesult independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the rv-n4hhwdpgba q k7hf +ug9) 6lliq,44oad if 7lh4h,qg a)d- u4h9w6gq+pn vl4fkbi a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fisl gck*k:v v6s4//yveghter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating? kvc: s*k4se6 /l/vgvy   rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntv7 0gb- /,ot uoo,.eemhdcie)able of variable speed. When the speed of the turntable is slowl.gb htue0io7),ocm-d/e,e v oy increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a.ud .ocqcqdx6ay+: wqvhyctj , x271 / roller coaster be traveling when upside down at the top of a circl c dchyx.6:, jvtqqwoay.c2u1 /7+dqxe
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crtki 3z* k(1wgzosses the rounded top of a hill (r zg *1itkz3wk(adius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per fuu8dqbv5y+q1s .fs* minute would a 15-m-diameter Ferris wheel need to make for the passengers to vqf5.*uqdsf bu y+s81feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of)x)nuji-i jrvpd+ g20 radius 1.10 m. At the lowest point of its motion the tension in the rope suppov)gu-j j2rx+pndi) 0 irting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the t(9(y mg ac7*wqwvtcp,j )zwx/hde24 axis of rotation is to exper mc zv(/c4,xjhg9e aqwy td)t(2*w7 wpience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in v1/6l 727 a8ss o2tj1 xi+ui lt6r ij0helkkmpa cylindrically walled "rt ssxret078ju 2 l+1jm6ioi ap1k2 6vkil hl7/oom." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless aij-ku2 bue pxvrvt8*t, 1ff2d2r-hockey tabldf -,jrx2e*2vu1v8b t pftk u2etop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight of t+a cne qxi :,on4365zbmo8gk the ball which revolves on a string 0.600 m long. In particular, find the magxo i6,4cnan5: mkq 8bz te3o+gnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly ban, euow sll:gh-7 0myi7ked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesaq)zm26p y mmmq(f1q/ $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310( wc29xv bk 6,jmcb(-fgzjg jw :kg1h( $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential an)zfyhdlg0z: ,- won6 sd centripetal components of the net force exerted on the car (by the ground:z-ny6lf z0 )sdwhg,o) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from 4d q/m e6lww:n-eg1cg the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what woulgce1 q4 6w/:n dw-gmeld the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a partp4u5c*c /bphymrr:9 cicular instant, its acceleration is 1.05uchymcrp b /9p c*4:r5 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spj61dn xd ;lgal:;*izqacecraft 12,800 km (2 Earth radii) above the Earth’s surface if itsd6jq x:l; zl*gid na;1 mass is 1350 kg.   

  At the surface of a certain ygdo5 fjyv / v-+e zq;vv;.6uvplanet, the gravitational acceleration g has a magnitude of 1vfjeov+y-/vd 6. g 5v;;yq zuv2 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the accelerationdpse-10i ijv- due to gravity on the Moon. The Moon's radius is 1.74 -d i0pvse-1ij $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Efpn7p:7v e+h:ns03 a*r/ vzyqzuld3iarth, but has the same mass. What is 3n 7 paq*3sdyzrv ul:+/n0ezfp7 v i:hthe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66eiet 97 fgh. 0evbn/ 4)zzysj; times that of Earth, but the same radius. z. te ezi7 g)ej0;sbf49/n hyvWhat is g near its surface?   

  Two objects attract each other gravitationallydc*34. 42abpkv lg rmg with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valpw,uf*tms/ f-p)um bfq c5kp5) j .p vl2m8uv5ue of g , the acceleration of gravity, at (a) 3200 m s ubw2. 8,-5m*)pfcv5f)tp/pupmlmfqvukj 5   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poinhwyb tj:v4.u-b42jc ft outside the Earth where thegravitational acceleration due to the Eaw4 4 :vfc.jbuhy t2b-jrth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has s:+n azl n:j* a-qah(jfive times the mass of our Sun packed into a sphere about 10 km in radius. Estimah(*::qj a-lnnz js+ aate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star,g ubcg:o87t2 cps4w+j which once was an average star like our Sun but is ngw+27 os:c8g 4uctjbpow in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while oxw) x8nvqfs6gh( 4u4d ypmi*3rbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface i 4vyw8sum4i * h()xq63fxgn dpn terms of g.   

  Four 9.5-kg spheres are located at( c .ild3 -mv*xy: m1wb:yfjzx the corners of a square of side 0.60 m. Calculate t ymjvb(* 1zifw:-:xxl.mdc3yhe magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the sa; tva)zdrrgk 3(9u:re0c/ogk01 h c ytm6sad4me side of the Sun. Calculate the totaoa3 rccut(d m g rz0v6k tkd;1r4heg0sa/)9:yl force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface ofh vc gf3)0 cm6p gb0p1z9hv5nf Mars is 0.38 of what it is on Earth, and that Mars’ radius is 30ggch v hp659f3mbv nf 1c0)pz400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the pe5zdyf;58w v yl5deboakn+(8yriod of the Earth and its distance from the Sun. [Nozd(ylyv nf 5+8ab5y dw58ek;o te: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the E q(y( nxs b4pe3l+yl nty*4gi0arth at a height ofy4sgn(4y+i3 q(n l 0l*p ybtex 3600 km.    $\times 10^3$

  The space shuttle releases a satellite io lzcln )o q((m-os9, j;lqie+nto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Ear z e+ol(9cs;,-mqnijlolq(o )th) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaces: h6b(dq4qb9e kak ,axe7li+ lhip rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceshipq+a4bielk7q hd:9k(xbl 6a , e’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in z sq:grik 72 wn0zea:3,a lm(za circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the sat:0nzsw37r z zla2am qi g,(ek:ellite?    s ~    min

  At what horizontal veloceq85 g1 tcy- 7robvhb7ity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular8e7bcq7 5- thyorb g1v orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to02 quw.2j2tz8w9 mt*d epky,i r1nwon orbit the Moon at an alwet*n2.jo ui0p 8q9t1zkmy,n 22drwwtitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the f:rqdbqh*vvf 76e+5gplanet. The inner radiug7v*v:5fq qdb6h e+f rs of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.57df;kvb9w g /.3zvo ku s (see Fig. 5–9). What is the ratov3k9/f gbdz;k.u7 wv io of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of theh,p9vlr:*y0mztg8 f e Earth's Moon in a space vehicle (a) 0ly9 *zmhgvf8 :p,rt emoving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binaryje* no8u r*z8kzmiou, -,:ocer 0za 0t-star system consists of two stars of equal mass. They are observed to be separated by 360 millionozeurj*a n0:8uzkz,*8 -c,te 0oorm i km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale rea n/i bat rg760kpv;bnd 5bu03bd for the weight of a 55-kg woman in an elevator that 6 bntnbbb05r ak/p03gdiu ; v7moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevatwztc8 k/tk2 3,n tdx7nor. The cord ca8knntkw,t x7cz /t3 d2n withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period T-6.ymbdehzs7 9acbg 7 , the density (mass/volume) of the zd-a7b7 9hg s6yb ec.mplanet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the peripw:,o x2s i4(3ozm;c;occ qzqod of 3i w cq;:oocopmq s;zxc (42,zan artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred m0(xc/y :ye pgsgzyh ;;eters across, orbits the Sun like the planets(y zyc; yxhep/;0gsg:. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofol 2q mtnzf(helacxx2a p .tbl314/)8k,)o hn 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It cg y5n)xtgq6cfdf1j+427o yje omes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third 7cdy ggx6 +ejq tfon14f2y)5jlaw is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cente* 7nptpqi+h.61 xjuaw r of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest mi ytb3+ v h3e),xt4adp:uyz7ooons of Juutp ta7zy3,)x+yv4b e: h3i dopiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and dist-c1/ j cr:tadtance of the Moon. -t:tr 1cc/ dja   $\times 10^{24}$

  Determine the mean distance from Jupiter for eop/ w- 7d1rwgf , 6-:0ctkedsuzjdh9 each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. uo cr 0ew/ds-ht:g6jz k,p 9-7dfewd 1Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars ahjj nl)+spi,p 79n cviy -db pu*,0x-mnd Jupiter consists of many fragments (which some space scientists think came from a planet that once orbitpbi xjpc,pv ,)- * dsjn7+m09uh iln-yed the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale desf6k/w6x7n 37v6 gg hap(pe-cd9wzmlgcribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent grave3l(w77a m6x /gdkzn pch9g fpgw-6 v6ity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an ar vfyiwm/;uo5j-vg4e ,c from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his vugjwm, ;e5f4o-/iyv swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth9 pyg ;.vq y 6i;cjtxs9z-u9gx’s surface will the acceleration of gravity be half what it is on the suj;9x-99 zqg 6ycxv .utys;g iprface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab qf ek2,+q+ gokms/bhu7a.i7 dhands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on7qk.2edbouh fg +m7ka, +qs /i one another?    $\times 10^2$

  Because the Earth rotad-zx dsm6wk8,d 9ma; qtes once per day, the apparent acceleration of gravity at the equator is slightly les8wqz d9 mx;-m6ad sdk,s than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft tra p;w;ndsd97huhhen p pw48 z45aaqg79veling directly from the Earth to the Moon experience zero net force becaudnzwnh gdu4 p57aw 97ha hesq9;4p8p ;se the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scakkex,5agn+e :p tzlo7q /u(t6le in an elevator, it says yxgz(o:u7q ep t,/kl+te 6a5n kour mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stdf, p5p )w1fg b5zipk6zl hx)2ation consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has adpp6wf k2ig5z l)b,x f)z5h 1p diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (F 6or:8hx; par)uh.4n:gdy juqig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms v4pzn8 ;hu (at0df9xqof its radius r, the acceleration due to gravity at its surface and th4p qdu9x;z haf(t0v8ne gravitational constant G.

A plumb bob (a mass m hanging onfo .aq7 g0bdrm e0:37fmlg7qlye7yu: a string) is deflected from the vertical by an angl f0gg7ym7 y3 ufaem7ll::qr. 0e7b qdoe $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of pih1j kqs02l76 3vt xr If the coefficient of static friction is 0.30 (wet pp0x1372vltqhjr 6ski avement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the zz23fe. al7bthb,8dx Earth were rotating so fast that objects at the equator were apparently weightb3lxd2teh8b z ,af.z 7less?    $\times 10^3$s

  Two equal-mass stars maintain a constud8) hx:lecb :ant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curvep (kknr+1+fb +iv8pee of radius 235 m. A lamp suspended from + fnke+peb1k( pv8+rithe ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Eaqv42fa9 gt:hjrth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.:f2 qahgt9 4vj9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the precw4uca v(v1u4 sence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 4uwuc vva14c( $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as i s6ws( cfvpw0t7swh*(t traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is (v6c 7 whswft0* p(swslargest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPSy4y cb(k qj+efi.tvq-j i(.( l) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in eaccjeb (lj(ki4+f-i qq .(yvt.y h of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is m;7bskhfed7pj 5bp g): eant to orbit7 ;kgj:dbp b 5fhe)s7p the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satewf)c /lk6yris rcv 1c:v 1xe79llite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 c 6ky wre1cx fr1/icv:7vs)l9km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is i bj +c f9cwuj7qn1qp51ts mean distance from j7qbwpc+n5cf1 j9q1uthe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could acto ,(j4ea/ zri4rfn0yrually "feel" yourself gravitationally attracted to someoiyazr( r,e fj404rn/o ne near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. mbzrys:wn4 ),vei f015-46) at a distance of about 30,000 light-years from th :b0nvw,m4)zriyes f 1e center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the cornexdzgb+fd jie mg3m f2zr28oq,670,pe rs of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at8mx0 6jff+z,2eqgzber ,p23im g7do d the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbi 77 qye8 drpf03brr-mmts the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleratdy61e*s lwi39zy s4feq + o -z36qmnjyion experienced by the tip of the 1.5-cm-long sweep second hand on o6dz33msnq6*yle 4z -j yis fe9wq +1yyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to s5 m1z iupa+z-uwing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: 5zau+mzp-1 iuSee Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway it i;:i ddsrm(2 f cq,7bh-sc(ss designed so that a car traveling atisqifm bd s(dt(,r;c2h -:sc7 speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars w)gs a5;y1vwfuhen negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed ofy1u)5 g;sawvf (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$